1. The recent Nobel Prize for the mRNA vaccines was awarded not on scientific merit but to encourage people to take the vaccines, and to reinforce the "safe and effective" message, according to a member of the Nobel committee. Yet the prize is presented as being for scientific achievement.
2. The population was told the plan for the first lockdown was for only two weeks. Off the record, health officials were briefing top executives of large local businesses to expect much longer lockdowns. Also, one of the senior public health officials in the Trump administration admitted in a book that she told Trump two weeks whilst knowing they were going to do it for much longer. The reason for the lie about the duration was because they thought people wouldn't accept it if they told the truth.
3. The virologists writing the Proximal Origin paper knew what they were writing probably wasn't true, but feared a "shitstorm", the impact on politics and the growth of "conspiracy theories" if they said they thought it came from a lab. So they deliberately misled the public.
Climatologists are the same way. In the ClimateGate emails there are parts where they agree to suppress contradictory evidence in order to avoid "diluting the message".
This backfired, repeatedly, and ultimately led to distrust of their statements when complete trust was necessary.